Conversion of Spin into Directed Electric Current in Quantum Wells

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VOLUME86, NUMBER19 P H Y S I C A L R E V I E W L E T T E R S 7 MAY2001

Conversion of Spin into Directed Electric Current in Quantum Wells

S. D. Ganichev,^1,2E. L. Ivchenko,²S. N. Danilov,¹J. Eroms,¹W. Wegscheider,^1,* D. Weiss,¹and W. Prettl¹

1Institut für Experimentelle und Angewandte Physik, Universität Regensburg, 93040 Regensburg, Germany

2A. F. Ioffe Physico-Technical Institute of the RAS, 194021 St. Petersburg, Russia (Received 31 January 2001)

A nonequilibrium population of spin-up and spin-down states in quantum well structures has been achieved applying circularly polarized radiation. The spin polarization results in a directed motion of free carriers in the plane of a quantum well perpendicular to the direction of light propagation. Because of the spin selection rules the direction of the current is determined by the helicity of the light and can be reversed by switching the helicity from right to left handed. A microscopic model is presented which describes the origin of the photon helicity driven current. The model suggests that the system behaves as a battery which generates a spin polarized current.

DOI: 10.1103/PhysRevLett.86.4358 PACS numbers: 73.50.Mx, 68.65. – k, 73.50.Pz, 78.30.Fs

The spin of electrons and holes in solid state systems is an intensively studied quantum mechanical property as it is the crucial ingredient for spintronics [1,2] and several schemes of quantum computation [3 – 5]. Among others, current investigations involve the spin lifetime in semiconductor devices [6 – 8] as well as the injection of spin polarized electrons (or holes) from semimagnetic semiconductor materials into semiconductors [9 – 11] or from ferromagnetic into nonmagnetic metals [12,13].

It is well known that spin polarized electrons can be generated by circularly polarized light [14,15] and, vice versa, that the recombination of spin polarized charged carriers results in the emission of circularly polarized light [10,11,14]. However, little is known about spin dependent photocurrents when a semiconductor is irradiated by circularly polarized light [15,16]. Helicity dependent photocurrents in semiconductors have been observed in bulk Te utilizing the peculiarities of the valence band structure (“camel back”) at the first Brillouin zone boundary and in bulk GaAs subjected to an external magnetic field [15]. A first indication of such a photon helicity dependent photocurrent in semiconductor heterojunctions was found in recent far infrared experiments onp-type GaAs兾AlGaAs heterojunctions containing a two-dimensional hole gas [17]. This preliminary experiment was discussed in phenomenological terms and lacked the microscopic connection to the carriers’ spin.

The experiments on quantum wells (QWs) described below uncover a novel property of an unbalanced spin polarization: its ability to generate a directed current where the current’s direction depends solely on the predominant spin orientation. This effect may be illustrated as an electron analog of mechanical systems where a rotational motion (“spin”) is transmitted into a linear one (“current”) like a rotating wheel on a hard surface. Below we point out that spin injection into quantum wells of zinc-blende – type ma- terial leads always to an electric current in the plane of the quantum well. The reduced dimensionality of quantum wells lowers the crystallographic symmetry and introduces k-linear terms in the Hamiltonian. Thesek-linear terms lift

the spin degenerate of energy bands in k-space which, in the case of an unbalanced spin population, results in a current flow. The conversion of the carriers’ spin polarization into an electric current has been observed in both n-type and p-type quantum wells as well as for different sym- metry classes. The observed spin photocurrent flows in the quantum well perpendicular to the direction of the incident circularly polarized light. The current reverses its direction by switching the sign of helicity of the radiation and hence the spin orientation of free carriers. The effect is quite gen- eral and has been observed for all semiconductor systems investigated. The experimental data can be described by simple analytical expressions derived from a phenomenological theory. To close the gap between the phenomenological (spinless) theory and the spin of the carriers we present a microscopic model for absorption by both direct (interband and intersubband) and indirect intraband optical transitions.

The experiments were carried out on heterostructures be- longing to two different classes of symmetry. Higher sym- metric structures of the point groupD2d were (001)-MBE grown n-InAs兾AlGaSb QWs with a 15 nm single InAs channel and (001)-MBE grown n-GaAs兾AlGaAs single heterojunctions. Structures of the lower symmetryCswere 共113兲A-molecular-beam-epitaxy (MBE) grown p-GaAs兾 AlGaAs single QWs and multiple QWs (MQWs) containing 20 wells of 15 nm width as well as p-GaAs兾 AlGaAs MQWs with 400 wells of 20 nm width grown by metal-organic-chemical-vapor-deposition on vicinal (001) substrates. The growth direction of the latter structures was found to be tilted by an angle of5^±with respect to the [001] crystallographic axis as has been verified by x-ray diffraction. Samples of n- and p-type with free-carrier densities between 10¹¹ and23 10¹² cm²² were studied in the range from liquid helium to room temperature. Two pairs of Ohmic contacts have been centered along opposite sample edges (see insets of Figs. 1 and 2). For optical excitation we used a high power far infrared pulsed NH3laser optically pumped by a transversely excited-atmospheric pressure CO2laser which yields strong linearly polarized 4358 0031-9007兾01兾86(19)兾4358(4)$15.00 © 2001 The American Physical Society

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VOLUME86, NUMBER19 P H Y S I C A L R E V I E W L E T T E R S 7 MAY2001

0 45 90 135 180

-6 -4 -2 0 2 4 6

[332]

y x [110]

Θ⁰= 0⁰ e

σ_- σ₊

0 0 0

0

(113)A- grown p- GaAs/AlGaAs MQWs

ϕ

j x / P ( 10-9 A / W ) -20 -10 0 10 20

x

Θ⁰= −30⁰ e

σ_-

σ₊

(001)- grown n- InAs/AlGaS

b QW

[110]

y

FIG. 1. Photocurrent in QWs normalized by the light power Pas a function of the phase anglewdefining helicity. Measure- ments are presented forT

苷

300K andl

苷

76mm. The insets show the geometry of the experiment. Upper panel: oblique incidence of radiation with an angle of incidenceQ₀

苷

230^±on n-type (001)-grown InAs

兾

AlGaSb QWs (symmetry classD2d).

The current jx is perpendicular to the direction of light propagation. Lower panel: normal incidence of radiation onp-type

共113兲A-grown GaAs兾AlGaAs QWs (symmetry class

Cs). The current jx flows along the

关1¯10兴

direction perpendicular to the mirror plane of theCssymmetry. Full lines are fitted using one parameter according to Eqs. (1) and (2).

emission at wavelengths lbetween 35 and280mm corresponding to photon energies ranging from 55 to 6 meV with power P up to 100 kW [18]. The radiation induces indirect (Drude-like) optical transitions in the lowest conduction subband of ourn-type samples and direct optical transitions between valence subbands (heavy hole – light hole) in thep-type samples. Crystalline quartzl兾4plates allowed us to modify the laser light polarization from linear to circular. The helicity P_circ of the incident light varied from 21(left handed circular, s₂) to 11 (right handed circular, s₁) according toP_circ 苷sin2w where w is the angle between the initial polarization plane and the optical axis of thel兾4plate.

The currentj_xgenerated by the circularly polarized light in the unbiased devices was measured via the voltage drop across a50V load resistor in a closed circuit configura- tion. The voltage was measured with a storage oscillo- scope. The measured current pulses of 100 ns duration reflect the corresponding laser pulses. In Figs. 1 and 2 we present measurements carried out at room temperature for (001)-n-InAs and共113兲A-p-GaAs兾AlGaAs quantum wells

j x / P ( 10-9 A / W )

-50 -25 0 25 50

0 2 4 6

x [110]

Θ⁰ e

(113)A- grown p- GaAs/AlGaAs MQWs right circularly polarized light (σ₊)

Θ

₀

-30 -20 -10 0 10 20 30 40

Θ⁰ e

(001)- grown

n-type InAs/AlGaSb QW right circularly polarized light (σ₊)

x [110]

FIG. 2. Photocurrent in QWs normalized by the light powerP as a function of the angle of incidenceQ₀for right circularly polarized radiations1measured perpendicular to light propagation (T

苷

300K, l

苷

76mm). Upper panel: n-type (001)-grown InAs

兾

AlGaSb QWs (D2d). Lower panel: p-type

共

113

兲

A-grown GaAs兾AlGaAs QWs (Cs). Full lines are fitted using one parameter according to Eqs. (1) and (2).

as representatives of the D_2d and C_s symmetry classes, respectively.

In (001)-oriented samples of the higher symmetry class D2d a signal proportional to the helicityPcircis observed only under oblique incidence and the photocurrent is perpendicular to the wave vector of the incident light. The reversal of the current direction when the polarization switches from left-handed to right-handed circular is clearly seen in the upper panel of Fig. 1. In samples of the lower symmetry classCsgrown on a (113)-GaAs surface, the spin photocurrent can be observed also under normal incidence as shown in the lower panel of Fig. 1. The same result is obtained for thep-type QWs grown on the vicinal (001)-substrate. Because of the misalignment the symmetry class is againC_s. The current flows always along the 关1¯10兴 direction perpendicular to the plane of mirror reflection of the point groupC_s, independent of the incidence plane of the laser beam. In Fig. 2 we take a closer look at the dependence of the photocurrent on the angle of incidenceQ0 of the circularly polarized laser beam. For (001)-oriented samples (D2d symmetry), a variation of Q0in the plane of incidence normal toxchanges the sign of the current jx for normal incidence, Q₀ 苷0, as can be seen in the upper panel of Fig. 2. The lower panel of 4359

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VOLUME86, NUMBER19 P H Y S I C A L R E V I E W L E T T E R S 7 MAY2001 Fig. 2 displays the angular dependence for (113)-oriented

quantum wells (C_s symmetry). A photocurrent proportional to the helicity P_circ was observed in all samples for all wavelengths and temperatures investigated. While we have also observed photovoltages across the other pairs of contacts, these voltages do not change sign upon the change of helicity. They are ascribed to the linear photogalvanic effect [15] and the photon drag effect [19]

which are outside the scope of the present investigation.

The solid lines in Figs. 1 and 2 are obtained from a phenomenological picture outlined below which perfectly describes the experimental observations. In this picture, the connection between the photocurrent,j, sensitive to the he- licity of light and the incoming light is given by the second- rank pseudotensorg asj 苷g ? eEˆ ²P_circwhere E is the amplitude of the electric field of the light andeˆ is the unit vector pointing in the direction of the light propagation [17]. The pseudotensorg can have nonzero components in gyrotropic systems which comprise quantum wells pre- pared on zinc-blende structures materials. For the higher symmetry D2d valid for quantum well structures grown along the principal axis [001], a photocurrent can be generated only under oblique incidence of irradiation. For the point group D2d the nonzero components of g are gxy 苷gyxwithx k关1¯10兴,y k关110兴. If共y,z兲is the plane of incidence, then the photocurrent is induced alongxwith j_x 苷g_xyt_pt_ssinQE₀²P_circ, (1) whereE0is the electric field amplitude in vacuum,tp and t_s are transmission coefficients after Fresnel’s formula for linearpandspolarizations [15],Qis the angle of refrac- tion defined by sinQ 苷sinQ₀兾n, andnis the index of re- fraction. In the low-symmetry QWs grown alongz k关hhl兴 with关hhl兴 ﬁ关001兴or [111], the point group isC_swhich contains only two elements, the identity and one mirror reflection plane normal to the 关1¯10兴 direction. In this case additionally the pseudotensor component gxz is nonzero allowing the generation of a photocurrent alongx k关1¯10兴 also under normal incidence of radiation. The corresponding contribution to the photocurrent is

j_x 苷g_xzt_pt_scosQE₀²P_circ. (2) The currents measured alongxas a function of the phase angle w (Fig. 1) and the angle of incidence Q₀ (Fig. 2) are in a very good agreement with the phenomenological expressions Eq. (1) for symmetryD_2d and Eq. (2) forC_s. Both figures show experimental data compared to calcula- tions which were fitted with one ordinate scaling parameter.

Microscopically a conversion of photon helicity into a spin photocurrent arises due tok-linear terms in the effective HamiltonianH^共¹^兲苷 b_lms_lk_mwherekis the electron wave vector, sl are the Pauli spin matrices, and blm are real coefficients. The coefficientsblmform a pseudotensor subjected to the same symmetry restriction as the pseudotensor g. The coupling between sl and the wave vector of the charged carrierskmas well as spin controlled selection rules, described below, yield a net current dependent upon circularly polarized optical excitation. The effect is

most easily conceivable for bothn- and p-type materials from the schematic band structure shown in Fig. 3. For the sake of simplicity we assume a band structure (two- dimensional dispersion) consisting only of the lowest conduction subband e1 and the highest heavy hole subband hh1. Thek-linear terms are taken into account only for the valence band and result in a splitting into two parabolas of different spin. In the case ofCs symmetry the splitting is given byEhh1,63兾2共k兲苷2共h¯²k²兾2mh兲 6 bkx[20].

First we consider direct optical transitions which, de- pending on the photon energy, may be of interband or intersubband type (heavy hole – light hole or heavy hole – heavy hole subbands inp-type materials). The theoretical con- cept of the model is the same for both types of transitions.

However, for intersubband transitions the k-linear terms, which are different for different bands and subbands, have to be taken into account for both subbands involved and complicate the picture. Hence, we concentrate on the interband excitations shown in Fig. 3a. While not directly illus- trating the transitions in ourp-type QWs, Fig. 3a makes the point more transparent than a discussion of the more complex intersubband transitions in the valence band.

Qualitatively the results are the same. In Fig. 3a the allowed optical transitions are froms 苷23兾2tos苷 21兾2

kx

j E

σ₊ σ₋

hh1 (+3/2) (-3/2)

kx kx

a

- +

e1 (±1/2)

kx kx

hh1 (+3/2) (-3/2)

E

f

e1 (±1/2)

kx

σ₊

(-3/2 -1/2)

hω

hh1 hh1

j

σ₊

(+1/2 +3/2)

b

0 0 ⁱ

FIG. 3. Microscopic picture describing the origin of spin polarized photocurrents. The essential ingredient is the splitting of the valence band due tok-linear terms. In (a)s₁ excitation induces direct transitions (solid arrows) froms

苷

23

兾

2

共

hh1

兲

tos

苷

21

兾

2

共

e1

兲

with unbalanced occupation of the positivek_x and negativekxstates resulting in a spin polarized photocurrent.

Fors2 excitation (dashed arrows) both the spin orientation of the charge carriers and the current direction get reversed. (b) A free electron transition (solid arrow) in the conduction bande1 via intermediate states in the valence subbands. Two represen- tative virtual transitions fors1 excitation are illustrated. One is an optical transition froms

苷

11兾2 to s

苷

13兾2 (dashed line, downward arrow) and a transition involving a phonon from s

苷

13兾2back to the conduction band (dash-dotted line, up- ward arrow). The other is a phonon transition from the conduction band to thes

苷

23兾2intermediate state inhh1and an optical transition froms

苷

23兾2tos

苷

21兾2. While the first route depopulates preferentially initial states of spin11兾2 for kⁱ_x.0, the second one populates preferentially the final state of s

苷

21兾2 states for kx^f ,0. This together with the unbalanced occupation of thek space results in a spin polarized photocurrent.

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VOLUME86, NUMBER19 P H Y S I C A L R E V I E W L E T T E R S 7 MAY2001 for the s₁ photon polarization and from s 苷3兾2 to

s 苷1兾2for thes₂polarization. Thesare the spin quantum numbers of the corresponding electron states. Under circularly polarized radiation with a photon energyhv¯ and for fixed value of k_y energy and momentum conservation allow transitions only for two values of k_x. For the s1

photons thesekxvalues of photogenerated electrons are k_x⁶ 苷 2m

¯ h²b 6

∑2m

¯

h² 共hv 2¯ Eg兲2k_y²1 µm

¯ h²b

∂2∏21兾2

, (3) whereEg is the energy gap,me,h are the effective masses of electrons and holes, respectively, andmis the reduced electron-hole effective massmemh兾共me 1mh兲. The corresponding transitions are shown in Fig. 3a by the solid vertical arrows with their center of “mass” shifted from the pointk_x 苷0by2b共m兾h¯²兲. Thus the sum of the electron velocities in the excited states, h¯共k¹_x 1k_x²兲兾m_e 苷 22共m兾m_e兲共b兾h¯兲, is nonzero and the contribution of k_x⁶ photoelectrons to the current do not cancel as in the case b 苷 0. Consequently, a spin polarized net current in the xdirection results. Changing the photon helicity from11 to21inverts the current because the “center of mass” of these transitions is now shifted to1b共m兾h¯²兲(see dashed arrows in Fig. 3a).

Now we consider indirect transitions. This situation is realized in our experiments onn-type QWs, where the photon energy is not high enough to excite direct intersubband transitions. Because of energy and momentum conservation intraband transitions can occur only by absorption of a photon and simultaneous absorption or emission of a phonon. This process is described by virtual transitions involving intermediate states. Transitions via intermediate states within one and the same subband do not contribute to the spin photocurrent. However, spin selective indirect optical transitions excited by circularly polarized light with both initial and final states in the conduction band can generate a spin current if virtual processes involve intermediate states in different subbands. Figure 3b sketches the underlying mechanism for s1 polarization. The two virtual transitions shown represent excitations which, fors1

helicity, “transfer” electrons from states with positive kx

to states with negativekx. The transfer results in a redis- tribution of the spins. This imbalance of occupiedkstates leads to a spin polarized current in thexdirection. Switch- ing the helicity from s₁ tos₂ reverses the process and results in a spin current in the opposite direction.

The picture of the spin photocurrent given so far involved the asymmetry of the momentum distribution of carriers. For a fully quantitative description of the spin polarized net current a possible asymmetry of the spin flip scattering rate of the carriers has to be included [16] which determines the decay of the photocurrent after pulsed excitation. In the present model of a spin degenerate conduction subband the decay is solely governed by momentum relaxation. Taking a spin split subband into account, the decay of the photocurrent is determined by both spin and

momentum relaxation times where the spin relaxation can be much slower than momentum relaxation.

In summary, the experiments carried out on different types of quantum wells have shown that circularly polarized light can generate a directed electric current even at room temperature. The microscopic picture given above requires that the generated current is spin polarized and suggests that the system can be considered as a source for spin polarized currents. We emphasize that in gyrotropic media withk-linear terms in the Hamiltonian, spin injection yielding an imbalance of spin orientation leads always to a current. As quantum wells based on III-V and II-VI compounds are gyrotropic, spin polarization causes in any case a current flow. The effect provides an easy access to investigate spin phenomena in low dimensional semiconductors.

The high quality InAs quantum wells were kindly pro- vided by J. De Boeck and G. Borghs from IMEC Belgium.

The technical support of M. Bichler is gratefully acknowl- edged. We also acknowledge financial support from the DFG, the RFFI, and the NATO linkage program.

*Also at Walter Schottky Institut, TU München, 85748 Garching, Germany.

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[20] The case of the D2d symmetry can be considered in a similar way. For the Cs symmetry described here the coordinate system isz k

关hhl兴

,x k

关1¯10兴

,y k

关ll共

2h兲兴¯ .

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